When the Subject of a subordinate clause is the same as the Subject of a main clause, we can usually omit the Subject from the subordinate clause.
In English, clauses with a tensed verb must have a Subject, and for this reason, whenever the Subject is missing we will see a non-tensed (non-finite) version of the verb. In addition, any tensed forms of BE will therefore be omitted if the Subject is missing:
- Although she was late, she still attended the meeting.
Although late she still attended the meeting. (Subject and tensed BE omitted)
After I studied for one year, I got 6.5 in my IELTS exam.
- After studying for one year, I got 6.5 in my IELTS exam. (No Subject, verb in non-finite -ing form)
We can of course also omit the Subjects of subordinate clauses which use to-infinitives when they are the same as the Subject in the main clause (because these, like -ing forms, are not tensed):
- For her to pass the exam, Paula will need to get over 60%.
- To pass the exam, Paula will need to get over 60%.
Although it is frowned upon by some style guides, and prescribed against in some exams (for example in SAT exams), in real life people often omit the Subjects of subordinate -ing clauses when they are clearly discernible from the context:
- Without going into details, the party was a complete disaster.
In the sentence above the understood Subject of going is me in other words, the speaker. The Subject of the main clause is, of course, the party. Nonetheless, there is nothing strange or odd about this sentence. In real life, writers should avoid omitting Subjects in subordinate clauses when it will jar the reader or cause confusion. The following is bad writing:
- Lying on the floor bleeding like that, I now wished I hadn't shot him.
The sentence above is bad, because we cannot be entirely confident whether the speaker or the person who was shot is lying on the floor. It doesn't matter that some grammars would allow this if the speaker was on the floor. In real life readers will be confused, because real language users might be referring to either person!
The Original Poster's Example
After studying for 1 year, I got 6.5 in the IELTS exam.
Because the Subject of the main clause is I, we will interpret the Subject of the subordinate clause as being the same person. The sentence is perfectly fine and perfectly grammatical.
A note about IELTS scores
If you are taking IELTS (International English Language Testing System), you will not be marked down for using grammar or vocabulary from standard Englishes from the UK, the USA or Australia, for example. It is after all an international English exam. The Original Poster uses in their example:
- I got 6.5 in the IELTS exam
This is completely grammatical in standard British English. Takers of this exam might come across advice that speakers of American English would use the phrasing:
- I got a 6.5 on my IELTS exam.
This is true. However, students undertaking an IELTS exam should not regard this as guidance for how to speak during an IELTS exam, or indeed guidance about how to write in an IELTS exam, if they are already familiar with the Original Poster's usage. Unlearning something completely grammatical for one standard discourse community - in favour of learning something that's ungrammatical in that discourse community but grammatical in another - is a waste of time. This is especially true for someone taking an exam which recognises different international standard varieties of English.
Perhaps a more useful illustration of this point is that - without fail - the actual IELTS exam board themselves use the Original Poster's phrasing in all of their published material. Here is an example from the Cambridge English Language Assessment publication Comparing scores on Cambridge English: Advanced (CAE) and IELTS:
Candidates who have secured a Cambridge English: Advanced (CAE) grade C are at Level C1 of the Common European Framework of Reference and can be expected to be comparable in ability with candidates who have secured 6.5 or 7.0 in IELTS.
Searches on Googlebooks or GoogleScholar will show that in IELTS is four to ten times more frequent that on IELTS.
The Ngram for "in IELTS" and "on IELTS" shows no results for "on IELTS" at all. If you click on the Ngram results for "in IELTS" you will find 19 pages of results referring to getting this or that score "in IELTS"
So, if you're going into your IELTS speaking exam, just stick with "got 6.5 in my IELTS exam"!!