Miles Jupp is hot when gyrating in desert (4,4)
I believe the answer is:
jump ship
'desert' is the definition.
(I know that desert can be written as jump ship)
'miles jupp is hot when gyrating' is the wordplay.
'miles' becomes 'm' (common abbreviation).
'hot' becomes 'h' (abbreviation eg on taps).
'when gyrating' indicates an anagram (letters dance or gyrate around).
'm'+'jupp'+'is'+'h'='mjuppish'
'mjuppish' is an anagram of 'JUMP SHIP'.
'in' is the link.
(Other definitions for jump ship that I've seen before include "Desert (originally from navy)" , "Defect" , "Unofficially, leave" , "(Sailor) desert" .)