High point in cold capital city close to crucifix (6)
I believe the answer is:
climax
'high point' is the definition.
'cold capital city close to crucifix' is the wordplay.
'cold' becomes 'c' (eg on taps).
'capital city' becomes 'lima' (I've seen this before).
'close to' indicates one should take the final letters (the close/ending of).
The last letter of 'crucifix' is 'x'.
'c'+'lima'+'x'='CLIMAX'
'in' is the link.
(Other definitions for climax that I've seen before include "High point" , "exciting finale" , "Most intense point" , "Peak of a performance" , "Turning point or culmination" .)