Consent to having a foreigner tailed (5)
I believe the answer is:
agree
'consent to' is the definition.
(agreeing is a kind of consenting to)
'a foreigner tailed' is the wordplay.
'foreigner' becomes 'greek' (I've seen this before).
'tailed' means to remove the last letter (to tail something can mean to remove its end).
'greek' with its final letter taken off is 'gree'.
'a'+'gree'='AGREE'
'having' acts as a link.
(Other definitions for agree that I've seen before include "Be of one mind" , "grant" , "Shake on it" , "Match; tally" , "Consent required" .)