Tenacious priest sent abroad (10)
I believe the answer is:
persistent
'tenacious' is the definition.
(thesaurus)
'priest sent abroad' is the wordplay.
'abroad' indicates an anagram.
'priest'+'sent'='priestsent'
'priestsent' anagrammed gives 'PERSISTENT'.
(Other definitions for persistent that I've seen before include "Pressing" , "Continual" , "not giving up" , "Determined" , "Not taking "no" for an answer" .)