Decrease space complexity, how will time complexity increase?
It depends on the problem.  There's no general rule.

The running time could be as low as $O(n+m)$: for some problems, there exists an algorithm with running time $O(n+m)$ and $O(1)$ space.  (Think about finding the maximum of an array with $n+m$ elements, for example.)

The best possible running time could also be as arbitrarily large.  For instance, think of analyzing connectivity in graphs: given a graph and two vertices $s,t$, determine whether there's a path from $s$ to $t$.  Let $n$ denote the number of vertices and $m$ the number of edges in the graph.  There is a simple algorithm with running time $O(n+m)$ and space complexity $O(n)$, namely, depth-first search.  However, there is no known algorithm whose running time is polynomial in $n$ and $m$ and that uses only $O(1)$ space.

See also https://cstheory.stackexchange.com/q/4556/5038 and https://cstheory.stackexchange.com/q/832/5038 for more technical details on this.

Terminology nitpick: problems have a complexity; algorithms have a running time.  the complexity of a problem is the running time of the best algorithm for that problem.