Ok, now we're getting somewhere.
This is a small dosing pump which, as far as we can tell from here, is running with virtually no back pressure.
If you can advise what the pressure is on the pump suction and discharge we would be in better shape, but lets assume it's less than 1 bar differential. the actual reading on the discharge might be 5 bar, but this is only just above the main pipe pressure.
The pump, although small, is working outside of its normal range and hence the leak ( from where?) might be due to that or just that the inlet isn't supposed to be a 4 bar. Small pump seals are not normally very sophisticated so it could just need tightening or replacing.
Long term you could regulate the inlet pressure down to say 2 bar, but it's probably easier just to insert an orifice plate somewhere between the pump discharge and the entry back into the pipe.
How do you or can you measure flow when it's fully piped up?
Like I said earlier, most of this can be solved next time by using a PD pump of some sort to pump the flow you want without having to worry about pressure. Small dosing pumps are often multi piston or diaphragm pumps.
Remember - More details = better answers
Also: If you get a response it's polite to respond to it.