Is there something like \renewcounter or \providecounter?

No, \renewcounter and \providecounter don't exist and they shouldn't.

By way of example, suppose you say

\providecounter{page}

\loop\unless\ifnum\value{loop}=4  % start the first loop
  \stepcounter{loop}  % counter loop +1
  % do something
  \recursiveloop{3}{page}  % call command to run second loop
\repeat

and \recursiveloop does \stepcounter{page}: chaos will ensue even if the loop is in a group, because \stepcounter, \addtocounter and \setcounter always act globally.

Of course you'd not use page, but what would happen if you choose a name already referring to some counter that's defined in a package you load and stores some important value?

Always allocate your own counters in the preamble or use the scratch counters provided by LaTeX (\@tempcnta and \@tempcntb).

By the way, don't use \theloop for numeric tests, but \value{loop}, which stores the value in a form which is independent from the value's representation.

If you really need \renewcounter then writing it is really simple: \def\renewcounter#1{\expandafter\ifcsname c@#1\endcsname\else\newcounter{#1}\fi \setcounter{#1}{0}. However, its use cases are indeed quite rare. The previous answer claims that it should “never” be used, which is, as quite often for such claims, an exaggeration; an example of a specific use case is an exam file, which includes some exercise files, each of which may define (through \renewcounter) their own, independent question counters.