I'd be interested to know how much sun this one gets planted where it is - roses always do better if they get as much sun as possible, and yours may be growing upwards in a desperate effort to find more sun or light. This one's ultimate height is 1.5 metres, which is quite tall for a hybrid tea rose, and might mean this is its growth habit anyway, though it does look particularly lanky, thin and weak.
That said, drastic action is called for - you need a good, sharp pair of secateurs and a bit of courage, because you've just got time to do this before you won't be able to, which is when we get into July. If you don't want to risk it now, you can do this last week of February or first week of March next year, or later in March if the weather is freezing cold, but omit the rose food at that time. Cut it down - if that wall next to it blocks light, then don't take it any lower than that. Remove all dead, thin, crossing, damaged and weak stems at the base of the plant, which, from looking at it, quite possibly means you'll just have two or three stems left, one of which is quite strong, and probably a couple of weaker ones. On the stems you're keeping, cut at a point where there is an outward facing bud, if you can find one (looks like a little bump on the stem) and angle your cut downwards, away from the bud. Get a specialist rose food, such as Toprose, and apply that immediately after cutting back (unless its early spring), according to the instructions on the box, turn it lightly into the soil at the base. Also get a bag of composted animal manure - spread some of that about an inch or two deep on the top of the soil around the base of the rose, without burying the stems any deeper than they are now.
Keep watered during very dry spells, but if the rose has been in situ for longer than two years, unless we have a drought lasting three months, its unlikely to need watering. Sit back and wait... and next year, in early spring, prune back again if its put on some growth, in exactly the same manner, except you don't need to take any main, thicker stems down so low if its growing well. Feed with the rose food in April and again in June, add more composted manure.
As for deadheading, you should use the secateurs for that too, cutting back to the nearest outward facing (away from the centre of the bush) bud above a leaf, again, angling the cut away from the bud. This might mean you remove as much as 10 inches of stem next year if its flowering and growing strongly, but more usually, 6 to 8 inches.
If the rose is in a relatively sunless position, it may still be thin and weak when it grows - but the treatment prescribed above will give it the best chance of growing healthily.