Sat, agitated, with phone going off in carriage (8)
I believe the answer is:
stanhope
'carriage' is the definition.
(I've seen this before)
'sat agitated with phone going off' is the wordplay.
'agitated' indicates anagramming the letters.
'with' says to put letters next to each other.
'going off' indicates an anagram.
'sat' with letters rearranged gives 'sta'.
'phone' anagrammed gives 'nhope'.
'sta'+'nhope'='STANHOPE'
'in' acts as a link.
(Other definitions for stanhope that I've seen before include "It may have only two wheels" , "Light horse-drawn carriage; Nineteen across (anag.)" , "carriage that has seat only for one" , "vehicle" , "old-fashioned conveyance" .)