There are multiple rules in the game that refer to something having an effect "in the first round of close combat". The first round of close combat refers to the first round of close combat that a single unit is involved in without disengaging due to fleeing, pursuing or other effects. This means that if a unit is engaged in combat with one unit and is later engaged by another unit, this only counts as the first round of close combat for the new unit, not any units that were already engaged in the combat.
Source: Warhammer Armies Project: Unofficial 9th Edition (v2.2)
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