Salamun Alaikum,
It does not have to be a ‘jilbab’. In verse 33:59, the Quran merely points at a type of garment worn in Arabia as an outer garment addressing a specific context.
However, the Quran does expect suitable coverage for women whereby the arms and legs are covered. This is clear from verse 24:60 where older women are permitted to discard their outer garments (thiyaab). Therefore, younger women would still be expected to maintain their outer garments (giving suitable coverage) when in unfamiliar company.
Both a jilbab (jalab) and thobe (singular of thiyaab) refer to outer garments in the context being discussed.
I hope that helps, God willing.
Joseph.