The most common and most likely answer to this crossword clue is the 6 letter word BECKON
I've seen this crossword clue in The Daily Telegraph
B
E
C
K
O
N
More clues leading to the result BECKON
Buddy explains!
The straight part
We know that "Invite to come over" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case invite to come over = beckon.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 BECKON mean?
BECKON noun- A sign made without words; a beck.
- A children's game similar to hide and seek in which children who have been "caught" may escape if they see another hider beckon to them.
- To wave or nod to somebody with the intention to make the person come closer.
- To seem attractive and inviting