You wrote:
It's important not to use IF checking every element whether it satisfies provided condition.
I cannot agree with this, unless you mean that once the sought element is found the rest of the elements should not be checked (possibly) using If. What I mean is that even if not using If itself there is going to be some kind of by-element checking until the target value is found.
One approach to what I believe you want:
SeedRandom[0]
a = RandomInteger[9, 10]
{7, 0, 8, 2, 1, 5, 8, 0, 6, 7}
p = FirstPosition[a, 5][[1]]
Join[Take[a, p], ConstantArray[0, Length@a - p]]
{7, 0, 8, 2, 1, 5, 0, 0, 0, 0}
Or more concise but less efficient:
Join[Take[a, p], 0 Drop[a, p]]
{7, 0, 8, 2, 1, 5, 0, 0, 0, 0}
Update
Based on your comments I believe this should be of use to you:
cTable[f_, n_] := FoldList[If[# == 0, 0, f @ #2] &, f @ 1, 2 ~Range~ n]
Example:
f = Mod[2 # + 1, 9] &;
cTable[f, 10]
{3, 5, 7, 0, 0, 0, 0, 0, 0, 0}
Note that f is only called four times here, not once for each element in the output. As proof we can add a Pause to it:
f = (Pause[1]; Mod[2 # + 1, 9]) &;
cTable[f, 10] // AbsoluteTiming
{4.010006, {3, 5, 7, 0, 0, 0, 0, 0, 0, 0}}
Because FoldList auto-compiles (by default for lists 100 or longer) this method should be acceptably fast. For example a list with nearly 5,000,000 zeros takes only a fraction of a second on my machine:
cTable[Mod[2 # + 1, 9] &, 5000000]; // AbsoluteTiming
{0.360001, Null}