Scattering of charge carriers and flicker noise in electrical transport are the central performance limiting factors in electronic devices, but their microscopic origin in molybdenum disulphide~(MoS$_2$)-based field effect transistors remains poorly understood. Here, we show that both carrier scattering and low-frequency $1/f$ noise in mechanically exfoliated ultra-thin MoS$_2$ layers are determined by the localized trap states located within the MoS$_2$ channel itself. The trap states not only act as Coulomb scattering centers that determine transport in both equilibrium ($eV< k_BT$) and non-equilibrium ($eV>k_BT$) regimes, where $V$ and $T$ are the source drain bias and temperature respectively, but also exchange carriers with the channel to produce the conductivity noise. The internal origin of the trap states was further confirmed by studying noise in MoS$_2$ films deposited on crystalline boron nitride substrates. Possible origin and nature of the trap states is also discussed.
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