Girl needing hot bath finally after game (4)
I believe the answer is:
ruth
'girl' is the definition.
(girl's name)
'hot bath finally after game' is the wordplay.
'finally' suggests the final letters.
'after' means one lot of letters go next to another.
'game' becomes 'RU' (rugby union).
The final letters of 'hot bath' are 'th'.
'th' put after 'ru' is 'RUTH'.
'needing' is the link.
(Other definitions for ruth that I've seen before include "- - Rendell, crime writer" , "She is followed by Samuel" , "distress once?" , "Babe -, US baseball player" , "Biblical character" .)