When Teemo Strategist is defending, does the ability proc first?

Yes, when Teemo, Strategist is defending, its ability triggers and resolves before any combat damage is calculated or applied.

According to RiftJudge FAQ #2687: "Teemo's ability resolves and deals damage before combat damage is calculated or applied, which can kill the attacking unit before it deals its combat damage."

Sequence of Events:

1. Teemo gains the "defender" designation (e.g., when revealed or when an opponent moves a unit to its battlefield).
2. Teemo's "When I defend" triggered ability is added to the chain.
3. Players have an opportunity to play [REACTION] cards (e.g., to buff Teemo, protect the attacker, or remove Teemo from the battlefield).
4. The ability resolves: you reveal the top 5 cards and deal damage to the chosen enemy unit.
5. If the attacking unit is killed by this damage, it is removed from combat before it can deal its own combat damage.
6. If the attacker survives, combat proceeds to the "Combat Damage Step" where units deal their damage.

Note: As per RiftJudge FAQ #3204, the triggered ability is separate from the unit itself. If your opponent uses a [REACTION] to remove Teemo from the battlefield after the ability triggers but before it resolves, the ability will still resolve (though it will not deal any damage if Teemo is no longer at the battlefield, as it requires targeting a unit "here").