Increase the number the bird is carrying (8)
I believe the answer is:
heighten
'increase' is the definition.
(heightening is a kind of increasing)
'number the bird is carrying' is the wordplay.
'number' becomes 'eight' (eight is a kind of whole number).
'the bird' becomes 'hen' (hen is a kind of bird).
'is carrying' means one lot of letters goes inside another.
'eight' put into 'hen' is 'HEIGHTEN'.
'the' is the link.
(Other definitions for heighten that I've seen before include "Move up" , "Intensify; make taller" , "Intensify, enhance" , "Make more intense - elevate?" , "Lift" .)