I liked Tasha's character too, from the start, and "got" her. She made a believable security officer and character in charge of security.
In some episodes, they take a little time to explore her role as a security chief and officer.
One example, in "Heart of Glory" the bridge is tracking the renegade Klingons and after finding them, Tasha asks Captain Picard if she should remain at her station or lead the security team herself to arrest them.
Then later you can see how she leads her security team, arrests them, and how she handles it.
Same thing for the Arsenal of Freedom. In the big goodbye we even got to see her sit in the chair, even though it's barely a second. In a way, it was nice to see.
On her personal side, I noticed the feeling she had with being security chief and balancing her femininity with being tough.
She did this in Hide and Q (when she got so frustrated she started crying, then felt embarrased) and in the Naked Now where she goes into Troi's quarters and talks about her clothes and how Troi seems to stays feminine.
She had no problem talking about her homeworld and how she grew up.
So like the others I wonder too how far her character would go throughout 7 seasons, would have been interesting.