Special welcome Yorkshire town cherished (3,6)
I believe the answer is:
red carpet
'special welcome' is the definition.
(special welcome for celebrities)
'yorkshire town cherished' is the wordplay.
'yorkshire town' becomes 'Redcar' (Redcar is a town in Yorkshire).
'cherished' becomes 'pet' (as in a pet project).
'redcar'+'pet'='RED-CARPET'
(Other definitions for red carpet that I've seen before include "one under the Queen?" , "see VIP on this?" , "VIP treatment" , "VIP walkway" , "sort of deferential treatment?" .)