Girl in game, losing heart (4)
I believe the answer is:
ruby
'girl' is the definition.
(girl's name)
'game losing heart' is the wordplay.
'game' becomes 'rugby' (rugby is a kind of game).
'losing heart' suggests removing the centre.
'rugby' with its middle taken out is 'RUBY'.
'in' acts as a link.
(Other definitions for ruby that I've seen before include "Girl's name - colour" , "Deep red - transparent gemstone" , "Stony girl" , "Jack perhaps" , "Vivid red" .)