What may apply grease and a lot of gooey stuff (3)
I believe the answer is:
gun
'what may apply grease' is the definition.
(as in a grease gun)
'a lot of gooey stuff' is the wordplay.
'a lot of' means to remove the last letter (a lot of but not all of the word).
'gooey stuff' becomes 'gunk' (gunk is something gooey or slimy).
'gunk' with its final letter taken away is 'GUN'.
'and' is the link.
(Other definitions for gun that I've seen before include "Artillery piece" , "Hired killer" , "Arm" , "What has barrel" , "Platform from which to shoot" .)