*All* connections at LHR require you to clear security of some form. This could be using the Flight Connections Centre (FCC), or by clearing immigration and customer, then going through 'normal' security.

T4-T3 is harder - the terminals are not connected. You can either get an airside bus (through the FCC at T4) or clear immigration/customs, and get the Heathrow Express between the two.

If you can't check through, then you'll have little choice in the matter, though.