Despicable sort's boring phone having numbered display (7)
I believe the answer is:
digital
'display' is the definition.
(digital display is a kind of display)
'despicable sort's boring phone' is the wordplay.
'despicable sort's' becomes 'git' (I can't explain this - if you can you should believe this answer much more).
'boring' is an insertion indicator (some letters must 'bore' a hole into other letters).
'phone' becomes 'dial phone' (dial phone is a kind of phone).
'git' going within 'dial' is 'DIGITAL'.
'having numbered' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for digital that I've seen before include "Type of clock" , "Of fingers or arithmetical figures" , "Of data expressed as a series of 0 and 1" , "(Watch) without hands" , "Key" .)