Hi DTK,
1d - 8 letter "board game" + 4 letter "piece on the board's" (really 3 letters but there is an apostrophe S) + 3 letter "with it" - definition is "skill in designing"
8a - anagram - definition is the whole clue.
13a - 2 letter "old" + 4 letter "Scottish side" (abbreviated) goes around/admitting an anagram of "riot" - definition is "showers" (as in people that show)