Hollow welcome given to start of the century (4)
I believe the answer is:
cave
'hollow' is the definition.
(caving is a kind of hollowing)
'welcome given to start of the century' is the wordplay.
'welcome' becomes 'ave' ('welcome' or 'farewell' - from Latin).
'given to' says to put letters next to each other.
'start of' suggests taking the first letters.
The first letter of 'century' is 'c'.
'ave' put after 'c' is 'CAVE'.
(Other definitions for cave that I've seen before include "Underground enclosure with surface access" , "Primitive dwelling" , "Hollow - warning" , "hole" , "Watch out" .)