Tiresome procedure, exercising dear pet (3,4)
I believe the answer is:
red tape
'tiresome procedure' is the definition.
'red tape' can be an answer for 'procedure' (red tape is a kind of procedure). I'm not certain of the 'tiresome' bit.
'exercising dear pet' is the wordplay.
'exercising' indicates anagramming the letters (letters exercise or move around).
'dear'+'pet'='dearpet'
'dearpet' anagrammed gives 'RED-TAPE'.
Can you help me to learn more?
(Other definitions for red tape that I've seen before include "Colourful bureaucratic procedure" , "Time consuming bureaucracy" , "Scarlet ribbon of bureaucracy" , "Unnecessary regulations" , "Petty official procedures" .)