What effect would raising reserve requirements while printing money have? It is generally accepted, that printing money will be inflationary, as it increases the money supply without a corresponding real growth of the economy. 

At the same time, if the central bank increases reserve requirements (or the official cash rate/bank rate) this decreases the money supply. 

So the question is, if a government, perhaps in a time of need, both prints money in order to carry out some project, and also increases reserve requirements/bank rate in order to conteract the inflationary effect, what are the likely follow on economic effects?
During the global financial crisis of 2008-2009, both the US and UK undertook quantitative easing (QE) in conjunction with a policy to fortify banks against risk by increasing reserve requirements.  So there are recent cases which illustrate what happens.

A rise in reserve requirements constrains a bank's ability to lend.  So it seems to counteract the idea of QE.  So why did both the US and UK implement these two seemingly antithetical policies?

Because the two policies also accomplish other objectives.  


An increase in capital requirements for banks was thought to be necessary to restore investor confidence in a badly shaken credit system (raising reserves was not done to counteract inflation).  Investors did not have confidence in the quality of assets on bank balance sheets, so requiring banks to retain cash deposits was one way of ensuring that banks had (a) a clear base of assets that were not obfuscated (e.g. subprime); and (b) limitations on how much risk (via lending) they could undertake.  So investors could feel safer about their deposits and the fundamental strength of the banking system.
Quantitative easing was aimed at injecting liquidity into an economy paralyzed by loss of confidence and liquidity, resulting in low spending and investment levels.  In order to offset the negative effects of raising capital reserves, the QE programs needed to be very large, which is why vast amounts of money were pumped into circulation in both countries.


The second part of your question is around follow-on economic effects.  Using the dynamics above you can infer the likely effects.

Raising capital requirements had the effect of exactly that.  It also had the effect of requiring larger volume of QE to counteract the drag on lending (in effect, money velocity or money multipler) cause by the higher reserve requirements.
Had QE not been sufficient to overcome the higher capital  reserves, you would have seen bank balance sheets swell while lending remained low....which is exactly what happened in the early to mid stages of QE while banks shored up their balance sheets before timidly starting to lend at risk again.