Gentle person stays up suffering, nursing cold (8)
I believe the answer is:
pussycat
'gentle person' is the definition.
(I know that pussycat are often gentle)
'stays up suffering nursing cold' is the wordplay.
'suffering' is an anagram indicator.
'nursing' is an insertion indicator.
'cold' becomes 'c' (abbreviation, eg on taps).
'stays'+'up'='staysup'
'staysup' is an anagram of 'pussyat'.
'pussyat' going around 'c' is 'PUSSYCAT'.
(Other definitions for pussycat that I've seen before include "Domesticated feline" , "One seeing owl" , "Tom perhaps" , "origin of part of 12 [GUITAR] ?" , "asked what's new in cinema?" .)