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A little bit confused with an "-ini" suffix in a turkish verb

It is not -ini suffix, it is -i suffix. It is used to change a verb into the object of the sentence. Beklediklerini= the things that they expect.
Uzmanlar: ''İspanya'dan tutarlı bir plan bekliyoruz.''
Uzmanlar İspanya'dan tutarlı bir plan beklediklerini söylüyor.

What a difficult question! I know someone can answer you better.:)

'Bekledikleri' as an adjective means 'that/which they await'

As in:

'bekledikleri tren' = 'the train which they await'
'bekledikleri cevap' = 'the answer that they expect'

As a noun, it means (in this case): 'the fact that they await'
(or more literally 'the act of awaiting, by them')

'Bekledikleri belli' = 'it is obvious (the fact) that they await'

'plan beklediklerini söylediler' = 'they said that they await a plan'

The -(n)i affix which is added, is due to the fact that here it is used as a direct object in the sentence, as is done with any other (defined) direct object. (As Gul pointed out earlier)