The Reconnect Line
Restart a contact who has gone cold, without the apology.
The reason most people never message an old contact is that they think the message has to explain and apologise for the silence. It does not.
The awkwardness is entirely on your side. They are not keeping score of who owed a reply. A short message with a reason for existing skips the whole problem, because it gives them something to respond to instead of a guilt-laden hello that requires them to manage your feelings about the gap.
Do not mention the gap
No sorry for going quiet, no it has been ages. Naming it makes it the subject and invites them to feel bad too.
Lead with the thing that reminded you
An article, a memory, news about their industry. The trigger is the message and it explains itself.
Ask nothing on the first message
No favour, no catch-up request. A first message with an ask attached reads as the reason you got back in touch.
Accept a short reply as success
Reopening the channel is the whole goal. The conversation can happen later or not at all.
Go deeper
What the paid version adds to this one.
The four opening lines that work, and why the obvious one does not
How to reconnect when you do genuinely need something
How long is too long, and when to leave it alone
Real reconnect threads, including the ones that got no reply