"What does this character want most?" is a good question to ask yourself whenever you make a character. It isn't the end of the world if you can't answer it, but I find that when I can answer it that the character is a lot more fun to play. After all, I know what it is they want most in the world.
The paradox of people is that innately we are all fundamentally simple creatures. We want things. We pursue those wants. We acquire those wants. We find new things to want. The paradox being that what we want, how we go about them, and all the conditions we put on our wants are very complex. As a simple show of how this complexity matters: two people could want to win a tournament. One person may insist on winning it fair though. The other doesn't care how much they cheat, as long as they win. This is the core conflict of a number of anime and even movies: the hero protagonist wants to win 'pure' and so they push through using their superior gamesmanship and love for the game to overcome the obstacles put in front of them by the person/team/group who is set on winning at all costs.
Now there are some caveats to this question. We're simple, and our characters are simple. But they're also complex, and ultimately we want a character that will go the distance of a game, right?
Caveat 1: The Want Should Not Be Easily Attainable or a Physical Thing
I've seen this problem with a number of characters across so many different games. The player comes in with a great character, and a solid goal. It is a great starting point for a new character because they have a reason to be where they are, a reason to go with the game, and a goal they want to achieve. The problem is the goal is too easily achievable.
In a large online game I ran, for example, a group of players came in with the goal being that they wanted to make enough money to replace the ship they had lost in a storm. It's not a bad goal, but do you see the problem? Because I did. What happens when they make the money to buy that replacement ship, but the game is still going on? Do they leave the game? What is their reason for staying? How will that impact them? In the moment all the players said they were fine with dealing with that later....only, cut to a few months later and one person had the money and wanted to go and suddenly things were weird and awkward as some characters no longer had a purpose, but others didn't want to retire their character and were almost mad at the people who had played their characters and pursued their goal.
You also see it in smaller games. An adventurer is looking to make money to help their family, or to buy a tavern. You have a couple adventures. You find your first treasure hoard. Suddenly your character has more money than they've ever seen before. More than enough to save the family farm and live the easy life. So why continue to put themselves in harms way? Money is especially easy in D&D 5e where the game is balanced around no magic items and doesn't have magic items for sale but you still get the money you would need in older campaigns to go and drop a couple hundred grand upgrading your stab-sticks.
Caveat 2: Emotional Wants Are Often Best
In my experience I've found more internal wants are the best. This can be as simple as "I want to be the best swordsman in the world" to as heartwarming as "I want to make my dad truly proud of me." These give the character an internal motivation to work towards. They give a thing to aspire to. Internal goals need to be met with internal growth, internal growth means character development. And this is a wonderful thing.
A Sub Goal That Conflicts
An instant formula for drama is to have 2 goals, but have them in conflict with each other. In the movie Troy, Brad Pitt's Achilles wears his primary goal of being remembered for all time on his sleeve. He is told that if he goes to Troy he will die but be remembered for all time, if he doesn't he will live a good life and be loved by family and friends but eventually forgotten. He goes to Troy. He inspires his men by telling them that immortality is theirs for the taking. He insults his foes by saying that no one will remember their name. He is there to be a legendary warrior. He is there to be remembered for all time.
And then he falls in love.
The conflict isn't super obvious at all times, but you can see how it happens. He starts taking actions that risk his ability to be remembered on behalf of this person he loves. When Troy falls, he sneaks in to try and save her instead of being part of the actual sacking of Troy that he believes to be his destiny to be remembered. And then, ultimately, he dies in trying to fulfill the love goal which is what gets him remembered for how he is found. The invincible Achilles, slain from what appears to be a single arrow in his heel.
What Happens When A Goal Is Achieved Is A Valid Question
Inigo Montoya in the Princess Bride has one real goal: to kill the six fingered man that slew his father when he was a boy. It is a goal he has somewhat abandoned, but it still drives him. At the end of the movie he resolves the goal which leaves him with the question of "what do I do next?" To paraphrase him, he says something along the lines of "I've been in the revenge business for 20 years, I don't know what to do without it."
As the end point of a movie, this is a perfectly valid way for things to go. The character has achieved their goal. They celebrate. They ride off into the sunset. Table Top RPGs are not as kind. Like in life, the character now has to grapple with what they do now. This can be something that is fun to explore with a character, but remember that the character's response may be to retire.
A character who was laser focused and driven on a single task, now in completing that task may lose direction. They can feel empty. They can feel changed. They're not the character you enjoyed playing anymore. And that's alright. Sometimes you get a different, better character out of that. Sometimes you don't until you retire the character.
It is a valid thing to want to explore. Just remember, you won't know which way it goes until you get there. And it might not go the way you want. Which is why the first bit of advice was to not build your character around an easily achievable goal.