mcshroom is likely to be right, but there are some checks you can do.
First off Tiagra comes in two versions,
SS and
GS. Both have official largest rear cog limit of 27T (while you are planning on using 34T). Secondly their official wrap capacities are 31T and 37T respectively. In your case since your intended cassette is taking up (34-11) or 23T of that capacity, your chainset's range (largest ring minus smallest) will also influence whether either will work.
Going back to the largest rear cog limit, despite breaching the official limit of 27T it will not be a problem if there is easily more than 16mm of clearance between the top pulley and existing largest rear cog when the chain is on it (because the radius of the 34T is 16mm larger than that of the 26T). That gap is adjustable to some extent by the
B screw.
Similarly, as you can see from the bottom of the article, the official wrap range can usually be exceeded, and of course depending on how important the 11T is to you the range requirement can also be changed potentially. But the first and easiest thing to observe is whether the top pulley will clash with the 34T. If it will, a Shimano mtb mech in SGS (long cage) form will offer you the maximum flexibility.