  A coloured braid group representation (CBGR) is constructed with the help of
some modified universal ${\cal R}$-matrix, associated to $U_q(gl(2))$ quantised
algebra. Explicit realisation of Faddeev-Reshetikhin-Takhtajan (FRT) algebra is
built up for this CBGR and new solutions of quantum Yang-Baxter equation are
subsequently found through Yang-Baxterisation of FRT algebra. These solutions
are interestingly related to nonadditive type quantum $R$-matrix and have a
nontrivial $q\rightarrow 1$ limit. Lax operators of several concrete integrable
models, which may be considered as some `coloured' extensions of lattice
nonlinear Schr${\ddot {\rm o}}$dinger model and Toda chain, are finally
obtained by taking different reductions of such solutions.
