Using local time frames to treat non-stationary real world signals as stationary yields Quasi-Stationary Signals (QSS). In this paper, direction of arrival (DOA) estimation of uncorrelated non-circular QSS is analyzed by applying a novel technique to achieve larger consecutive lags using coprime array. A scheme of virtual extension of coprime array is proposed that exploits the difference and sum co-array which can increase consecutive co-array lags in remarkable number by using less number of sensors. In the proposed method, cross lags as well as self lags are exploited for virtual extension of co-arrays both for differences and sums. The method offers higher degrees of freedom (DOF) with a larger number of non-negative consecutive lags equal to MN+2M+1 by using only M+N-1 number of sensors where M and N are coprime with congenial interelement spacings. A larger covariance matrix can be achieved by performing covariance like computations with the Khatri-Rao (KR) subspace based approach which can operate in undetermined cases and even can deal with unknown noise covariances. This paper concentrates on only non-negative consecutive lags and subspace based method like Multiple Signal Classification (MUSIC) based approach has been executed for DOA estimation. Hence, the proposed method, named Virtual Extension of Coprime Array imbibing Difference and Sum (VECADS), in this work is promising to create larger covariance matrix with higher DOF for high resolution DOA estimation. The coprime distribution yielded by the proposed approach can yield higher resolution DOA estimation while avoiding the mutual coupling effect. Simulation results demonstrate its effectiveness in terms of the accuracy of DOA estimation even with tightly aligned sources using fewer sensors compared with other techniques like prototype coprime, conventional coprime, Coprime Array with Displaced Subarrays (CADiS), CADiS after Coprime Array with Compressed Inter-element Spacing (CACIS) and nested array seizing only difference co-array.