In that they're both implementations of Common Lisp, but is there a deep connection between the two than that? Not that directing more attention to clasp is a bad thing!
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Clasp author here - Clasp uses SICL's Cleavir compiler.
SICL is being developed in a modular fashion: I believe clasp uses SICL’s compiler framework Cleavir for its own compiler. (I’ve also heard that ABCL and ECL have considered reimplementing their compilers with Cleavir)