Add the hit points from leveling up to current hit points
The Dungeon Master's Guide (1993) for Advanced Dungeons & Dragons, 2nd Edition on Effects of Experience, in part, says
When a character earns enough experience to attain the next level for his character class, he immediately gains several benefits (unless the optional rules for training are used). The character gains an additional die of hit points (or a set number of hit points at higher levels). These [hit points from leveling up] are added to both his current hit point total and his maximum number of hit points. (48–9 and emphasis mine)
It appears that in the campaign the question describes, you're not using the optional training rules, so these rules should apply.
However, this is only the default method. The DMG presents several alternatives on how and when to award experience and on how and when to allow leveling up, so you needn't feel constrained by these rules if a different way works better for you.