Climb a castle, destroyed after end of siege (8)
I believe the answer is:
escalate
'climb' is the definition.
(thesaurus)
'a castle destroyed after end of siege' is the wordplay.
'destroyed' indicates an anagram.
'after' says to put letters next to each other.
'end of' says to take the final letters.
The last letter of 'siege' is 'e'.
'a'+'castle'='acastle'
'acastle' anagrammed gives 'escalat'.
'escalat'+'e'='ESCALATE'
(Other definitions for escalate that I've seen before include "Amplify" , "Increase in intensity or extent, like trouble brewing" , "rocket" , "mushroom" , "Ramp up" .)