As I said in a comment, I think you should make the two functions in methods of class BoardHandler. This will give you better encapsulation and it's fairly easy to do, here's how:
class BoardHandler:
    def __init__ (self, size, board):
        self.size = size
        self.board = board
    def ask_size(self):
        try:
            self.size = int(input("Which size would you want?"))
        except ValueError:
            print("Wrong! try again")
            ask_size()
    def getNewBoard(self):
        board=[]
        for i in range(self.size):
            board.append([' ']* self.size)
        self.board = board
    def resetBoard(self):
        for x in range(self.size):
            for y in range(self.size):
                self.board[x][y] = ' '
        n=int(size/2-1)
        self.board[n][n] = 'B'
        self.board[n+1][n] = 'W'
        self.board[n][n+1] = 'W'
        self.board[n+1][n+1] = 'B'
    def drawBoard(self):
        HLINE = '  ----------------------------------------'
        for y in range(self.size):
            print(y+1, end=' ')
            for x in range(Q):
                print('| %s' % (self.board[x][y]), end=' ')
            print('|')
            print(HLINE)
If you want to keep them outside the class for some reason, you will need to modify each of them to accept a BoardHandler class instance as an argument:
def resetBoard(board_handler):
    for x in range(board_handler.size):
        for y in range(board_handler.size):
            board_handler.board[x][y] = ' '
    n=int(board_handler.size/2-1)
    board[n][n] = 'B'
    board[n+1][n] = 'W'
    board[n][n+1] = 'W'
    board[n+1][n+1] = 'B'
def drawBoard(board_handler):
    HLINE = '  ----------------------------------------'
    for y in range(board_handler.size):
        print(y+1, end=' ')
        for x in range(Q):
            print('| %s' % (board_handler.board[x][y]), end=' ')
        print('|')
        print(HLINE)
This assumes your program creates a single BoardHandler class instance, and does all operations to that object.