damalig
former / then
Referring to a specific point in the past; existing or valid at that time.
Mein damaliger Chef war sehr streng, aber fair.
My former boss was very strict, but fair.

former
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former / then
Referring to a specific point in the past; existing or valid at that time.
Mein damaliger Chef war sehr streng, aber fair.
My former boss was very strict, but fair.

'Damalig' (former/then) is derived directly from the adverb 'damals' (back then), which means 'at that time.' If you know 'damals', you can easily work out the meaning of 'damalig'.
Ich besuchte damals oft meine Großeltern. Mein damaliger Schulweg war sehr kurz.
Back then, I often visited my grandparents. My school route at the time was very short.
The adjective 'damalig' (former/then) is used almost exclusively before a noun (attributive use). Using it after the noun as part of the predicate is uncommon and sounds unnatural.
Die damalige Regierung hatte mit großen Problemen zu kämpfen.
The government at the time had to deal with major problems.
The word 'damalig' (former/then) always needs a clear time reference in the past that has already been mentioned in the conversation or text. It refers to a situation at a specific, already known point in time.
Als ich 1995 studierte, war das Leben anders. Meine damaligen Freunde sehe ich heute noch.
When I was studying in 1995, life was different. I still see my friends from that time today.
old
'alt' and 'damalig' can both refer to something from the past. 'alt' is more general and can mean 'former' or 'previous', for example with an old school or a former boss. 'damalig' means more precisely: at that specific earlier time. It is often used when talking about a concrete time or situation from the past. Learners may confuse the words because both sound connected to the past. A practical rule is: 'alt' also works without an exact time; in meaning, 'damalig' usually needs a reference to a specific point in time or period.

Der damalige Chef kannte alle Mitarbeiter persönlich.
The boss at the time knew all the employees personally.
Meine alte Lehrerin arbeitet jetzt an einer anderen Schule.
My former teacher now works at another school.