`exec {myvar}>file` will open a file descriptor that can write to `file`, and then store that file descriptor in the variable `$myvar`, so you can then redirect additional commands to it with `>$myvar` or `>>$myvar`.

From the bash man page:

> Each redirection that may be preceded by a file descriptor number may instead be preceded by a word of the form {varname}. In this case, for each redirection operator except >&- and <&-, the shell will allocate a file descriptor greater than or equal to 10 and assign it to varname. If &- or <&- is preceded by {varname}, the value of varname defines the file descriptor to close. If {varname} is supplied, the redirection persists beyond the scope of the command, allowing the shell programmer to manage the file descriptor himself.