Splurge in US city, initially with round of drinks (4,3)
I believe the answer is:
lash out
'round of drinks' is the definition.
The definition suggests a verb in its base form which matches the answer.
'splurge in us city initially' is the wordplay.
'splurge in' becomes 'shout' (I am not sure about this - if you are sure you should believe this answer much more).
'us city' becomes 'la'.
'initially' says to put letters next to each other.
'shout' put after 'la' is 'LASH OUT'.
'with' is the link.
Can you help me to learn more?
(Other definitions for lash out that I've seen before include "Attack, verbally or physically" , "severely run down" , "React violently" , "Attack with blows or words - using whip?" , "Vigorously attack" .)