Guarantee offers assurances to leader's husband (4)
I believe the answer is:
oath
'guarantee' is the definition.
(thesaurus)
'offers assurances to leader's husband' is the wordplay.
'leader' indicates taking the first letters.
'husband' becomes 'h'.
The first letters of 'offers assurances to' is 'oat'.
'oat'+'h'='OATH'
(Other definitions for oath that I've seen before include "One sworn" , "Sworn declaration" , "Vow, sworn word" , "Swear word" , "Strong language" .)