Men-only party in The Palace perhaps is the icing on the cake for one of those in The Park (5,4)

I believe the answer is:

royal stag

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

'the palace perhaps is the icing on the cake for one of those in the park' is the definition.
I can't judge whether this defines the answer.

'men-only party' is the wordplay.
'men only' becomes 'royal' (I am not sure about this - if you are sure you should believe this answer much more).
'party' becomes 'stag' (stag party is a kind of party).
'royal'+'stag'='ROYAL STAG'

'in' acts as a link.

Can you help me to learn more?

(Other definitions for royal stag that I've seen before include "Ruminant" , "deer" .)

I've seen this clue in the Irish Times (Crosaire) and the Irish Times.

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.