The most common and most likely answer to this crossword clue is the 4 letter word PECK
I've seen this crossword clue in The Times
P
E
C
K
Buddy explains!

The straight part
We know that "Kiss/Hollywood great" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case kiss/hollywood great = peck.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does PECK mean?
PECK noun- An act of striking with a beak.
- A small kiss.
- To strike or pierce with the beak or bill (of a bird).
- To form by striking with the beak or a pointed instrument.
- To strike, pick, thrust against, or dig into, with a pointed instrument, especially with repeated quick movements.
- To seize and pick up with the beak, or as if with the beak; to bite; to eat; often with up.
- To do something in small, intermittent pieces.
- To type by searching for each key individually.
- To type in general.
- To kiss briefly.
- One quarter of a bushel; a dry measure of eight quarts.
- A great deal; a large or excessive quantity.
- To throw.
- To lurch forward; especially, of a horse, to stumble after hitting the ground with the toe instead of the flat of the foot.
- Discoloration caused by fungus growth or insects.