The primer seals are a softer material (possibly silicone) than the main seal between the head and the square body. They can perish and leak, often when the pump is switched off it fills up the side hollows and drips down the side of the body.
They're not hugely expensive (approx £10) and easy to replace. I followed a YouTube video where someone replaced this with a cheaper nitrile seal, but wouldn't recommend it. These are much less soft and while they stop the leak, you won't be able to press the priming button. I managed to crack the abs head fitting mine back together because the nitrile seal didn't compress well as the motor/primer pushed into the plastic head, so it leaked when switching the pump off. This was despite using silicon lubricant.
Thankfully as the head is abs I could repair it with a thin sheet of abs from ebay and some pure acetone to make an abs glue slurry and seal the crack in the head after drilling the end of the crack.
Having spent hours messing about with this filter I wished I'd spent the extra fiver on the proper primer button seal! But it works now, and I learnt how to repair abs.
If it's suckling in air the main body seal has probably gone. It can also weap from the join when the pump is switched off. At least thats what mine did.
Places that can leak: main body seal, primer button seal, small o ring in the flow monitor, taps o rings, finally within the taps themselves there are two really chunky o rings which push against the ball valves. To get to the latter you have to split the two sections of the taps in half, which is a little fiddly. I'd only consider these if it's obviously leaking from the body of the taps. I reclaimed an old filter that had spent fifteen + years in the garage and this chunky oring must have been dry and got twisted the first time I turned the tap. By splitting the taps into two parts washing a lubricating the oring and reassembling it all worked fine again.
Hope you get it fixed.