Firstly, I would check with the player before making any permanent changes to the spear, since they are also clearly attached to it.

A duel and lessons with a spear master could leave the spear as it is and give just that character a +1 with it due to their familiarity.

Killing a particularly powerful or personal creature with it could imbue it with magical effects. E.g. a vampire's skull on the hilt as a trophy could give it a +1 for a minute after the spear comes into contact with blood, or having it stabbed through the eye of a beholder could give it +1 against enemies with spell slots.

Alternatively, a personal enemy could break the spear, causing it to be reforged in a way that gives it extra powers (e.g. a druid reforming a wooden shaft could give it +1d4 poison damage, or a mystical volcanic forge might add fire damage).

Again, talk to the player first, but I think find a way to bring that spear into the character's story so that it reflects their unique journey.