It's past tense with て form, but I can't make sense of it after the first て.
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I can see why this construction is difficult to understand, as there are multiple different meanings that can result from both ～て form and ～くる and there's no easy way to work out which one is being used in each case. I'll describe the most common/likely interpretation below but if there's a particular example you're struggling to understand please post it together with the context it came from.
The first て here is just linking the two events 言われた ⇒ やってきた in successive temporal order, with the nuance that the second was a result of the first.
言われる: to be told something (passive form of 言う)
やってくる: Think of this as a single verb. It basically means the same as 来る in its literal, physical sense - i.e. to come (to a place). The やって adds a sense of having come with the purpose of doing something in particular. We don't really have a concise way to express this in English, so it will often be translated simply as "come", but for the purpose of understanding the expression you can think "come on a mission". I might sometimes translate this as "come down" or "come along" to inject the extra nuance in a subtle way depending on the context/style of the speaker etc.
The above is counter-intuitive because it does not really correspond to what you would expect given the standard meaning of やる and behaviour of verbs in て form before くる. So you really have to just remember it as a single set phrase, i.e. a complete verb in itself.
Also, please use sparingly in daily conversation. My feeling is it's used more to talk about others, and especially when describing fictional characters. Using it about one's self could give off an air of self-importance, so if used about one's self will often have a tone of irony. It could also sound a bit disrespectful when talking about others, which is why it is mostly seen talking about third parties outside of a given situation such as fictional characters.
Putting it all together, you have (in the translation below I assume the subject is "I" but it could just as easily be "he", "she", "they", etc.):
Xと言われてやってきた。 I came because somebody told me X.
To give a more concrete example, here's a sentence I found in a movie review for the movie バナナ・パラダイス on this page after searching Google for "言われてやってきた":
台湾はバナナがたくさん食べられて天国のようなところだと言われてやってきた２人だった These two came to Taiwan after hearing that it was like a paradise where one could eat loads of bananas.
The nuance conveyed by the やって part here is that they came to eat lots of bananas. As you can see it's not really necessary in the English as it's understood from context, but if one wanted to reflect it in the English and maybe add some flair to the translation one could write "These two came to Taiwan hoping to fill their bellies after hearing..." or something like that.