Gaps happen. Supply runs out, life intervenes, a vial expires before you finish it. Restarting is a normal event and it is worth handling deliberately rather than just picking up where the log stopped.
First, establish the length of the gap precisely. Not "a few weeks". The date of the last dose and today's date. That single number determines almost everything about how to think about the restart, and it is the fact the log exists to preserve.
Second, check what changed while you were away. A new vial almost certainly means a new concentration, and the unit count you remember is attached to a vial that no longer exists. Re-derive it from milligrams. This is the single most common restart error, and the reason a log should always record mg alongside units.
Third, write a restart marker in the log. A row that says restart, with the date and the gap length. Without it, a future reader sees a continuous sequence with a strange hole in it and cannot tell whether the hole was a break or a missing entry.
Fourth, decide the restart dose before the day arrives, not on the day. Deciding in the moment, with the syringe out, is how people end up resuming at whatever they were on before without thinking about whether that still makes sense.
Fifth, expect the first few entries to be worth more detail than usual. Side effect notes after a gap tell you more than the same notes during a steady stretch, because the contrast is sharper.
I keep restart markers in the same table as everything else in the Peptide Tracker & Calculator, with the gap in days in the note field. It costs nothing and it makes the shape of the history obvious at a glance.