  Two energetic millisecond pulsars (MSPs) within globular clusters (GC),
J1823-3021A in NGC 6624 and PSR B1821-24 in M28, have been recently discovered
to emit pulsed GeV gamma-rays. These MSPs are expected to eject energetic
leptons. Therefore, GCs have been proposed to produce GeV-TeV gamma-rays as a
result of the comptonization process of the background radiation within a GC.
We develop this general scenario by taking into account not only the diffusion
process of leptons within a GC but also their advection with the wind from the
GC. Moreover, we consider distribution of MSP within a GC and the effects
related to the non-central location of the dominating, energetic MSP. Such more
complete scenario is considered for the modelling of the GeV-TeV gamma-ray
emission from the core collapsed GC M15 and also for GCs which contain recently
discovered energetic MSPs within NGC 6624 and M28. The confrontation of the
modelling of the gamma-ray emission with the observations with the present
Cherenkov telescopes and the future Cherenkov Telescope Array (CTA) allows to
constrain more reliably the efficiency of lepton production within the inner
magnetosphere of the MSPs and re-accelerated in their vicinity. We discuss the
expected limits on this parameter in the context of expectations from the
pulsar models. we conclude that deep observations of GCs, even with the present
sensitivity of Cherenkov telescopes (H.E.S.S., MAGIC, VERITAS), should start to
constrain the models for the acceleration and radiation processes of leptons
within the inner pulsar magnetosphere and its surrounding.
