Prime minister's detailed record at first appals (7)
I believe the answer is:
dismays
'appals' is the definition.
(I've seen this before)
'prime minister's detailed record at first' is the wordplay.
'prime minister's' becomes 'mays' (I've seen this in other clues).
'detailed' means to remove the last letter (the tail of the word is removed).
'record' becomes 'disc' (eg a CD, compact disc).
'at first' says to put letters next to each other.
'disc' with its final letter taken off is 'dis'.
'mays' put after 'dis' is 'DISMAYS'.
(Other definitions for dismays that I've seen before include "Appals" , "Troubles" , "Fills with discouragement" , "alarms" .)