Desperately determined in entrance and exit
I believe the answer is:
do-or-die
'desperately determined' is the definition.
(I've seen this before)
'entrance and exit' is the wordplay.
'entrance' becomes 'door' (door is a kind of entrance).
'and' means one lot of letters go next to another.
'exit' becomes 'die' ('die' can be a synonym of 'exit').
'door'+'die'='DO OR DIE'
'in' acts as a link.
(Other definitions for do-or-die that I've seen before include "Involving a final desperate attempt" , "Desperately determined" , "Recklessly determined" , "Make a final desperate attempt to achieve" , "'Theirs not to reason why, theirs but to . . . . . . .' (2.2,3)" .)