The most common and most likely answer to this crossword clue is the 4 letter word BADE
I've seen this crossword clue in The Daily Telegraph
B
A
D
E
More clues leading to the result BADE
Buddy explains!

The straight part
We know that "invited" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case invited = bade.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 BADE mean?
BADE verb- To issue a command; to tell.
- To invite; to summon.
- To utter a greeting or salutation.