I have no idea what your curve is or the reason the gap exists, so this is a guess. The approach to both is to find the ends of the first part of the curve, and connect them to the beginning of the second part.
If you know where the gap is, try this:
x1 = linspace(0, 1);
y1 = sin(x1*3*pi);
x2 = x1 + 2;
y2 = cos(x2*4*pi);
figure
subplot(2,1,1)
plot(x1, y1, 'g')
hold on
plot(x2, y2, 'g')
hold off
subplot(2,1,2)
plot(x1, y1, 'g')
hold on
plot(x2, y2, 'g')
plot([x1(end) x2(1)], [y1(end) y2(1)], '-r') % Connect Ends With Red Line
hold off
If your data have a region of one or more consecutive NaN values, try this:
x3 = linspace(0, 5);
x3(40:60) = NaN;
y3 = exp(-(x3-2.5).^2);
nanv = find(isnan(y3)); % Find Region With ‘NaN’ Values
figure
plot(x3, y3, 'g')
hold on
plot(x3([nanv(1)-1, nanv(end)+1]), y3([nanv(1)-1, nanv(end)+1]), 'r') % Connect Ends With Red Line
hold off
