The most common and most likely answer to this crossword clue is the 7 letter word EVOKING
I've seen this crossword clue in The Times
E
V
O
K
I
N
G
More clues leading to the result EVOKING
Buddy explains!

The straight part
We know that "Calling up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case calling up = evoking.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 EVOKING mean?
EVOKING verb- To call out; to draw out or bring forth.
- To cause the manifestation of something (emotion, picture, etc.) in someone's mind or imagination.
- To elicit a response.