Change stdout for shell to pipe

With exec >LOG 2>&1 I can change stdout and stderr for the current shell, so all following commands will inherit those file descriptors. Is there a way to change stdout/stderr for the current shell to a pipe? I've tried exec | gpg -aer 0x6aabe354 in the hope to replace current stdout with gnupg, encrypting the output of the remaining script, but I received cleartext output and an empty PGP message instead, so clearly this is not the correct syntax.