Then you need to get some. More bases are
vital.
The next actual lab is the 'Science Laboratory', which is locked behind Promotion II. So quite some ways off. Getting more Biolabs and Intel Centers (and perhaps even another HQ if you're swimming in money) is the way to go in early game.
There are also a number of sidegrades (Jumpsuit, Night Ops Suit, Bio-Exo Suit) to the Kevlar vest, losing out on some (frontal) armour but giving other benefits. Pretty much all of those are gated behind the Workshop (and some other requirements), which is partway to Promotion II. The most difficult part, usually.
There's also the Mongorn skin suit that's basically an improved leather coat and only requires enough Mongorns. And looks cool.
I don't think you're up to destroying the cults if you're still wearing leathers. In general, if you leave the cults alive you get 'punished' with mansions (and thus cultist aircraft) and endless anti-cultist missions (plus some mid-game fuckery like hybrid bases). If you're patient, on the ball with your air game and can take down manors en masse (easier said than done), that's essentially free money and other loot. Some pretty nice loot, actually.