The most common and most likely answer to this crossword clue is the 7 letter word TWEETER
I've seen this crossword clue in The Times
T
W
E
E
T
E
R
More clues leading to the result TWEETER
- Stagger around with the Speaker?
- Speaker taking to social media?
- Social networker using rather cute short name
- Speaker, one using social media?
- Speaker who gives brief messages
- Speaker‘s pretty terse before start of speech
- Speaker‘s dainty half-sister
- 1’s bird?
- Look likely to fall about with user of social media
- Be hesitant about watts needed for loudspeaker
Buddy explains!

The straight part
We know that "Social networker" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case social networker = tweeter.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 TWEETER mean?
TWEETER noun- An electronic speaker designed to produce high-frequency sound.
- One who posts messages ("tweets") on the social networking site Twitter.