Hail tearfully? (5)
I believe the answer is:
greet
'hail' is the definition.
(thesaurus)
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for greet that I've seen before include "Welcome; cry (Scots)" , "Say hello, hail" , "Address on arrival, say hello" , "Meet and salute" , "Acknowledge" .)