For clarity, there is no global Answer to this question because, as noted, it depends greatly on the local circumstances. However, Singapore is somewhat special in that there are no domestic flights so the entire terminal is on the other side of Immigration and 'Security' is essentially at the gate. So, 'airside' is conceptually different there as opposed to say London or Hong Kong.
When arriving, you will be directed away from the Gate's Departure Lounge and into the main Terminal which is essentially all a Transit area. You can wait for her there.
When the GF arrives, you won't be able to get right up to the gate, but close enough depending on the configuration.
There's more information in the edit history, I just don't remember enough right now and won't be able to refresh for ~4 months.