Incline to admit having to go inside (8)
I believe the answer is:
gradient
'incline' is the definition.
(thesaurus)
'admit having to go inside' is the wordplay.
'admit' becomes 'grant'.
'having' is an insertion indicator.
'to go inside' becomes 'die' (I am not sure about this - if you are sure you should believe this answer much more).
'grant' going around 'die' is 'GRADIENT'.
'to' is the link.
(Other definitions for gradient that I've seen before include "Treading (anag) - slope" , "Bank" , "Perhaps one in ten" , "Slope or incline" , "Third OT book" .)