Tries to win over bowlers, say, in competition (5,2)

I believe the answer is:

chats up

I'm a little stuck... Click here to teach me more about this clue!

'tries to win' is the definition.
I can't tell whether this defines the answer.

'bowlers say in competition' is the wordplay.
'bowlers say' becomes 'hats' (bowler is a type of hat).
'in' means one lot of letters goes inside another.
'competition' becomes 'cup' (I've seen this before).
'hats' put within 'cup' is 'CHATS UP'.

'over' is the link.

Can you help me to learn more?

(Other definitions for chats up that I've seen before include "Flirts with" , "Gets friendly with" .)

I've seen this clue in The Guardian.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.