Equally determined to gain an advantage (5)
I believe the answer is:
asset
'an advantage' is the definition.
(I've seen this before)
'equally determined' is the wordplay.
'equally' becomes 'as' (synonyms).
'determined' becomes 'set' (similar in meaning).
'as'+'set'='ASSET'
'to gain' is the link.
(Other definitions for asset that I've seen before include "It's an advantage to declare" , "Item conferring advantage" , "Useful thing or person" , "Useful or valuable quality or possession" , "Someone or something of value" .)